At what distance can an island be seen at sea?

Some interesting info here.

I could give a estimate. But if this is for homework it would lack the precision your instructor probably expects.

it would depend greatly on the humidity and general outside temp

Also, define “small sailboat”. How high is the deck from the waterline? Or are you up on the mast?

I can tell you that you can see a hell of a lot further from the Signal Bridge of an aircraft carrier than from the flight deck, which in turn has a longer view than from the Hangar deck or most of the sponsons.

So give us a height of the vantage point.

I was on a 40’ sailboat doing a delivery one time. It was really foggy, so I can say from personal experience that, in the fog, it doesn’t matter how big the mountains are. I would estimate visibility at about…20 feet. :D

Roughly 3 miles to the horizon.

Each thousand meters of distance the curvature of the earth drops off about a ten meters. Ten thousand feet is about 3000 meters. So at 30,000 meters you should be able to see the highest peak. This is about 22 miles. I was in the Navy and can verify this.